Solubility measurement and modeling of hydroxychloroquine sulfate (antimalarial medication) in supercritical carbon dioxide

A supercritical fluid, such as supercritical carbon dioxide (scCO2) is increasingly used for the micronization of pharmaceuticals in the recent past. The role of scCO2 as a green solvent in supercritical fluid (SCF) process is decided by the solubility information of the pharmaceutical compound in scCO2. The commonly used SCF processes are the rapid expansion of supercritical solution (RESS) and supercritical antisolvent precipitation (SAS). To implement micronization process, solubility of pharmaceuticals in scCO2 is required. Present study is aimed at both measuring and modeling of solubilities of hydroxychloroquine sulfate (HCQS) in scCO2. Experiments were conducted at various conditions (P = 12 to 27 MPa and T = 308 to 338 K), for the first time. The measured solubilities were found to be ranging between (0.0304 × 10–4 and 0.1459 × 10–4) at 308 K, (0.0627 × 10–4 and 0.3158 × 10–4) at 318 K, (0.0982 × 10–4 and 0.4351 × 10–4) at 328 K, (0.1398 × 10–4 and 0.5515 × 10–4) at 338 K. To expand the usage of the data, various models were tested. For the modelling task existing models (Chrastil, reformulated Chrastil, Méndez-Santiago and Teja (MST), Bartle et al., Reddy-Garlapati, Sodeifian et al., models) and new set of solvate complex models were considered. Among the all models investigated Reddy-Garlapati and new solvate complex models are able to fit the data with the least error. Finally, the total and solvation enthalpies of HCQS in scCO2 were calculated with the help of model constants obtained from Chrastil, reformulated Chrastil and Bartle et al., models.

Supercritical carbon dioxide T System temperature (K) T c Critical temperature (K) v 1 , v 2 , v s Molar volume of solvent, solute and solute (m 3 /mol) V 1

Energies of interaction
There has been greater attention in the recent past about the application of supercritical carbon dioxide in micronization of pharmaceuticals [1][2][3][4][5] . The drug administration is decided by the size of the particle. As we know, intravenous drug delivery requires particles size ranging from 0.1 to 0.3 μm, inhalation delivery requires 1-5 μm and oral delivery requires 0.1-100 μm and the smaller the size of the particles, greater chance of a drug being absorbed by the human body, which helps in reducing the drug dosage 1 . Conventional particle reduction techniques result in products that are in the particulate range, for example jet mills provides product particles in the range 5-45 μm, hammer mill provides product particles in the range 25-600 μm, on the other hand supercritical fluids (SCFs) technology provides product particles in the range 0.1-600 μm 1 . But, to apply SCFs technology, solubility data of a specific drug in the desired SCF is required for the selection and design of suitable SCF process that reduces the particle size, thus the solubility will determine the operating condition of the process [6][7][8] . Present work is focused on the both solubility measurement and modelling of hydroxychloroquine sulfate (HCQS) in scCO 2 . This drug was originally developed in United States (US) to counter malaria in the year 1949 9,10 . HCQS is considered as better alternate to chloroquine, due to less toxicity. It is also used for the treatment of Rheumatoid Arthritis (RA) and Systemic Lupus Erythematosus (SLE) 9,11 disease. A recent study conducted by Pishnamazi et al., on the solubility of chloroquinein scCO 2 has inspired us to take up this task 12 . Since 1950, chloroquine has been in use to treat malaria, however, hydroxychloroquine, a chloroquine analogue has a better safety profile due to a hydroxyl group on the side chain and is used in the treatment of connective tissue disorders 13 . We believe this study helps to implement SCF technology to get the desired drug size particles of HCQS and which may help to reduce the drug dosage in treatment. To expand the use of solubility data, modelling is performed with literature models and new solvate complex models.
This work is carried out in two steps. In the first, HCQS solubility in scCO 2 solvent is determined and in the second, data measured in the first stage are correlated with literature models. The models employed are solid-liquid equilibrium, Chrastil, reformulated Chrastil, Méndez-Santiago and Teja (MST), Bartle  Solubility measurement details. SCF-solubility of the drugs was experimentally measured via two broad classes of saturated solution-based methods, where solubility measurement can be done either (1) statically or (2) dynamically 14 . In the present work, a UV-vis spectrophotometer was utilized to statically examine the equilibrium solubility data of HCQS in a setup presented in Fig. 1. This experimental setup has already been validated in our previous work with alpha-tocopherol and naphthalene 15 . The solubilities were measured with the help of an equilibrium cell. Thermodynamically, the method employed may be regarded as an isobaric-isothermal method 14  www.nature.com/scientificreports/ value with high precision (i.e., ± 0.1 K and ± 0.1 MPa). Complete details about the equipment and measurement procedures are presented elsewhere  . However, the description of the equipment and the methodology employed in establishing solubility data are briefly presented in this section. The scCO 2 is pumped to the equilibrium cell and drug sample and scCO 2 are thoroughly mixed and allowed to attain equilibrium. It is observed that the equilibrium is attained in 60 min. To ensure equilibrium solubility, the experiments are performed with fresh samples at various time intervals. For a specified temperature and pressure in each experiment, the drug sample is contacted with scCO 2 and stirred thoroughly in an equilibrium cell until a specific time (5 min, 10 min, 20 min, 30 min, 40 min, 50 min and 60 min) and the solubility readings are recorded. It is observed that the solubility is independent of time after 30 min. However, for solubility measurement, the samples are collected after 1 h. For each sampling a 600 µL volume saturated sample is collected via a collection valve in a deionized water preloaded sample vial. After discharging of each sample, the sampling valve was cleaned with 1 ml of deionized water. Drug sample solubility is estimated with the following formula: where y 2 is solubility of the drug in scCO 2 , n drug and n CO 2 are number of moles of the drug and CO 2 in the sampling loop, respectively. The following formulas are used in data conversion where C s is concentration of the drug in g/L. V 1 = 600 × 10 -6 L and V s = 5 × 10 -3 L are sampling loop and vial volumes, respectively. M s and M CO 2 are drug and CO 2 molecular weights, respectively. ρ 1 is density of scCO 2 at each experimental condition, as presented in Table 2.
(1) y 2 = n drug n drug + n CO 2 www.nature.com/scientificreports/ Solubility is also described as The solubility and mole fraction relation is described as The HCQS's solubility is quantified in the UV-Visible spectrophotometer (Model UNICO-4802) with the help of deionized water (conductivity ≤ 5 µS m −1 ) as collection solvent with the wave length of 220 nm at UV spectrum.

Modelling
Although there are several approaches in modelling solubility data, solid-gas equilibrium (known as equation of state (EoS) approach), solid-liquid equilibrium (SLE, also known as expanded liquid equilibrium approach) and empirical modelling are commonly used in literature for the data correlation [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50] . For EoS approach critical properties of both solvent (scCO 2 ) and solute (HCQS) are required, whereas the SLE approach requires only melting temperature and melting enthalpy of the solute, but empirical modelling doesn't need any such information. HCQS is a typical compound and it is not possible to estimate its critical properties due to the presence of H 2 SO 4 in its structure. Due to this fact EoS modelling is not persuaded. On the other hand, experimental Table 2. Solubility of HCQC in scCO 2 at various temperatures and pressures. y 2 and S are mole fraction of HCQS in scCO 2 and equilibrium solubility (g/L), respectively. The experimental standard deviation was obtained by S y k = n j=1 (yj−y) 2 n−1 . Expanded uncertainty (U) and the relative combined standard uncertainty (u combined /y) are defined, respectively, as follows: (U) = k*u combined (k = 2) and In this research, u(x i ) was considered as standard uncertainties of temperature, pressure, mole fraction, volumes and absorption. P i , sensitivity coefficients, are equal to the partial derivatives of y equation (Eq. 1) with respect to the x i . a Standard uncertainty values are u(T) = ± 0.1 K and u(p) = ± 1 bar. The value of the coverage factor k = 2 was chosen on the basis of the level of confidence of approximately 95%. www.nature.com/scientificreports/ melting temperature and melting enthalpies of HCQS are available; due to this reason expanded liquid modelling is explored. For empirical modelling the density of scCO 2 , and system temperature and pressure are required; since they are readily available, it is also persuaded here. For empirical modelling, six commonly used solubility models are considered and those models have a varying number of parameters in their equations ranging from three to seven. The modelling purpose of some empirical models is to check the self-consistency of the measured data and to estimation some of the thermodynamic information of the dissolution process. In general, solubility of solids in SCFs is visualized in terms of solvate complex formation; therefore, a new set of solvate complex models is proposed for the better data fitting/correlation. More details about all the models considered in this work are presented in the following subsections.
Solid-liquid equilibrium (SLE) models. In this approach the HCQS solute is assumed to be infinitesimally dissolved in the scCO 2 solvent. At equilibrium, the drug fugacity in solid phase is equal to that of fugacity of drug in scCO 2 phase. From this criterion, the following solubility expression is proposed [51][52][53][54][55][56][57] .
From the literature, there are several models for this approach. However, Wilson activity coefficient model is considered for the data regression 58 .
The required γ ∞ 2 is obtained from Wilson model and the relevant expressions are as follows: where On combining Eqs. (10)-(15), we get Commonly used empirical models. Chrastil's model 59 . In the year 1981, Josef Chrastil presented a model for the solubility of solids/liquids in SCF. The main basis of the model is a solvate complex formulation based on a simple reaction. According to Chrastil, solubility is explained by c 2 = c 2 (κ, ρ 1 , T) , where κ is association number, ρ 1 is solvent density (scCO 2 ) and T is temperature. Chrastil proposed Eq. (19) An alternative from of Eq. (19) is Eq. (20) 60 where y 2 is solute solubility in mole fraction.
in Eq. (21), R denotes universal constant of ideal gas, M ScF is molecular weight of solvent, f * is reference pressure and A 2 and B 2 are the Reformulated model constants. 62 . The MST model is used to check the consistency of the data. All the data falls around a single straight line when T ln y 2 P − C 3 T versus ρ 1 is established. MST model is expressed as Eq. (22) where A 3 to C 3 are the model constants.  64 . It is the model developed based on the degree of freedom analysis based on drug compounds. According to this model, solubility, y 2 = y 2 (T r , P r ) , is expressed as Eq. (24), where T r and P r are reduced temperature and pressures, respectively.

Reddy-Garlapati model
where A 5 to F 5 are the model constants.
Sodeifian et al., model 65 . It is another recently proposed empirical model. According to this model, solubility,y 2 = y 2 (T, P, ρ 1 ) , can be calculated by where A 6 to F 6 are the model constants.
(17) One assumption that v A P RT is expressed as Zv A ρ 1 M where ρ 1 is the density of the supercritical phase and the second assumption is refereed to negligible term v A P Sub A RT(~ 10 -8 -10 -9 ) [since the sublimation pressures are very low and their order is about (~ 10 -3 -10 -4 ) and the drug molar volume is also about the order (~ 10 -4 )] [67][68][69][70] . (39) is rearranged as Eq. (40) Further, on rearranging Eq. (40), we get Eq. (41) We know solubility, y 2 , is related to cluster mole fraction y AB κ as Eq. (43) 68,69 Thus the solubility is expressed as Eq. (44) κ ′′ is a function of reduced density, given by Eq. (45) 71 Combining Eqs. (44) and (45)  The obtained deviations are indicated in terms of an average absolute relative deviation percentage (AARD%).
The entire regression task was done using (MATLAB 2019a®) version software, also this can be performed by nonlinear regression methods with the same results 84,85 .

Results and discussion
The experimental device used for the measurement of HCQS solubility in scCO 2 is accurate and reliable. It was successfully tested to reproduce the solubilities of naphthalene in scCO 2 and alpha-tocopherol in scCO 2 systems and the same was reported in our earlier work 15 . The solubility values reported for alpha-tocopherol in our previous work, are the average of three replicate measurements with relative standard deviations lower than 5.7% 15 . The solubility values of naphthalene reported in our previous work are also the average of three replicate measurements with relative standard deviations lower than 6.5% 15 . Table 2 shows the measured solubilities of HCQS in scCO 2 at various conditions and the density of the scCO 2 , obtained from the NIST data base 73 . From solubility data, it is clear that present system (HCQS+scCO 2 ), does not exhibit the usual retrograde phenomenon. Affecting solvent density and solute power, the temperature was found to impose a dual impact on solubility in scCO 2 depending on how the solute vapor pressure and solvent density are balanced. In this respect, increasing the solution temperature may enhance the solute vapor pressure, thereby contributing to stronger solvating power of SCF. At the same time, a rise of temperature may lower the scCO 2 density which is known to depreciate the overall solvating power of the fluid. The mole fraction versus pressure isotherms on Fig. 2 suggest an enhancement in the solubility of drug upon elevating the temperature. This proves the dominant role of the solute vapor pressure in determining the solubility behavior irrespective of the pressure. Reports by other researchers confirm the results of the present work regarding the effect of temperature on the solubility in scCO 2 74-76 . From Table 2 and Fig. 2, it is clear that when temperature is raised from 308 to 338 K, there is a clear indication of a rise in solubility from 0.0304 × 10 −4 to 0.1398 × 10 −4 at 12 MPa (i.e., 4.6 folds' increase) and at 27 MPa from (42)  www.nature.com/scientificreports/ 0.1459 × 10 −4 to 0.5515 × 10 −4 (i.e., 3.8 folds increase). At the same time, at 12 MPa, the density of scCO 2 changes from 769 to 338 kg m −3 at 308 and 338 K, respectively. Similarly, the density of scCO 2 at 27 MPa changes from 914 to 783 kg m −3 at 308 and 338 K, respectively; which means that there is decrease in density at 12 MPa (low pressure) (i.e., 338/769 = 0.4395) and there is increase in density to some extent at 27 MPa (higher pressure) (i.e., 783/914 = 0.8567). Thus, the solubility behavior of HCQS in scCO 2 is highly nonlinear. This kind of high nonlinearity behavior has been observed with amlodipine besylate-scCO 2 in the recent past 28 . This kind of high nonlinearity behavior can't be captured with simple models. Thus models having more adjustable constants are required to fit the data and this would augment the justification for the need of development of new models. All the regression results are summarized in Table 3 Table 3. Regression results of all models used in this research.

Model Correlation parameters AARD% R² R² adj
Solid-liquid equilibrium (SLE) α = 4.9285 × 10 -3 ;β = − 1.156 × 10 -3 ;    www.nature.com/scientificreports/ ability of commonly used three parameter models are found to be inferior when compared to Sodeifian et al., and Reddy-Garlapati models. This may be due to a smaller number of parameters in the models; on the other hand, the correlating ability of the solvate complex models is quite good. However, among all empirical models, Reddy-Garlapati model is the best model. The newly proposed solvate complex models have more adjustable constants, and thus their predictions are also good. From the solvate complex model's constants, it is interesting to note the behavior of association number. When association number is treated as a linear function of reduced density, the obtained average association number for the solubility data is κ ′′ ave = 2.21, which is lesser than that of the conventional Chrastil's model κ = 3.89. But, when association number is treated as quadratic function of reduced density, the obtained average association number for the solubility data is κ ′′ ave = 3.78, and it is matching well with association number of Chrastil's model. From those results and from literature arguments, we can infer that association number is quadratic function of ρ r so that is apparent than other forms and its correlations are reliable 71,79 . Thus, association number as quadratic function of ρ r is recommended for the data interpolation.
Further, a comparative analysis is done to determine the best model for HCQS-scCO 2 system. Since, a varying number of parameters are involved in the equations considered in the work, Akaike Information Criterion (AIC) and corrected AIC (AIC c ) [80][81][82][83] are used to identify the best model. AIC alone is used when data points are more than forty; on the other hand, AIC c is used when data points are less than forty. In the present there are only twenty-four solubility data points in our hands; hence, AIC c is used for identifying the best model. AIC c is defined as Eq. (52) where N is solubility data points, Q is number of model constants, and SSE is error sum of squares. From the least AIC c value, the best model is identified. The lower the AIC c value the greater the accuracy of the model, and it is independent of the number of parameter. All the AIC c values are reported in Table 5. From results, Reddy-Garlapati and the new solvate complex models are observed to be the better models.

Conclusion
Solubilities of solid HCQS in scCO 2 solvent were measured at various conditions ranging from P = 12 to 27 MPa and T = 308 to 338 K. The measured data's range is from 0.0304 × 10 -4 to 0.5515 × 10 −4 in terms of mole fraction. Three forms of solvate complex models explored in this study are reasonable in estimating solubility and among the three the best model is observed to have AICc and AARD values − 595.4 and 10.08% respectively. Among

Data availability
On request the data may be obtained from the corresponding author.  www.nature.com/scientificreports/